Related papers: The number of dimensional fundamental constants

We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points associated to such a definition.

We present here a note which synthesizes our previous ideas concerning some problems in cosmology, and the numerical correspondences between the physical constants that we could deduce.

Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…

A numerical coincidence relating the values of the cosmological, gravitational and electromagnetic fine structure constants is presented and discussed in relation to the apparent anthropic fine-tuning of these three fundamental constants of…

Several authors have recently explored the idea that physical constants such as c and G might vary over time and have formulated theories describing this variation that can address a range of cosmological problems. Such work typically…

Astrophysical observations suggest that the fine structure constant (alpha) may (or may not) be evolving over the cosmological time scale. This raises a much debated question: is alpha variation due to the variation of the speed of light…

A theory of the cosmological constant Lambda is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the…

An action for a string and a particle with two timelike dimensions is proposed and analyzed. Due to new gauge symmetries and associated constraints, the motion of each system in the background of the other is equivalent to effective motion…

The common nature of the dark sector - dark energy and dark matter - as shown in [1] follows readily from the consideration of generalized Newtonian potential as a weak-field General Relativity. That generalized potential satisfying the…

The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…

A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous…

We discuss the fundamental constants of physics in the Standard Model and possible changes of these constants on the cosmological time scale. The Grand Unification of the strong, electromagnetic and weak interactions implies relations…

Defined by Lord Kelvin as the science of measurement it is described a fundamental fact of physics. The so called `natural' units represent the unique system of units conveniently used in the realm of High Energy Physics. The system of…

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…

Astronomical observations have a unique ability to determine the laws of physics at distant times in the universe. They, therefore, have particular relevance in answering the basic question as to whether the laws of physics are invariant…

Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional…

The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper…

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d=2 the answer is three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4 the…

We consider two problems that have vexed physicists for several decades -- dark matter and the cosmological constant. The problem has been that the former has not been detected while the latter gives a far higher value than detected by…

In physics we encounter particles in one of two ways. Either as fundamental constituents of the theory or as emergent excitations. These two ways differ by how the particle relates to the background. It either sits on the background, or it…